Refined exponential stability analysis of a coupled system

Mohammed Safi (1, 2) , Lucie Baudouin (1) , Alexandre Seuret (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

The objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.

Mots clés: integral inequalities; Lyapunov stability; Transport equation

Domaines: Automatique / Robotique

Mohammed Safi, Lucie Baudouin, Alexandre Seuret. Refined exponential stability analysis of a coupled system. IFAC World Congress, Jul 2017, Toulouse, France. ⟨hal-01496136⟩